Optimal AD-Conversion via Sampled-Data Receding Horizon Control Theory

Abstract

This paper presents novel results on the joint problem of sampling, reconstruction and quantization of analog signals. Existing literature on this topic deals exclusively with band-limited signals in sampled form. Our key departure from earlier results is that we deal with continuous time reconstruction of not necessarily band-limited signals. Our approach utilizes concepts and tools from optimal sampled-data and receding horizon control theory. The key conclusion from the work presented here is that, in the case under study, the optimal quantizer design problem can be partitioned into two sub-problems, namely (i) the design of an optimal analog pre-filter followed by sampling and (ii) an optimal quantizer, which works directly on the pre-sampled signals. Simulation results are presented which illustrate the performance of the optimal A-D converter designed via these principles.